Problem: Solve for $x$. Enter the solutions from least to greatest. $2x^2 - 16x + 14 = 0$ $\text{lesser }x = $
Solution: $\begin{aligned} 2x^2 - 16x + 14&= 0 \\\\ 2(x^2-8x+7)&=0 \end{aligned}$ Now let's factor the expression in the parentheses. $x^2-8x+7$ can be factored as $(x-1)(x-7)$. $\begin{aligned} 2(x-1)(x-7)&=0 \\\\ x-1=0&\text{ or }x-7=0 \\\\ x=1&\text{ or }x=7 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= 1 \\\\ \text{greater }x &= 7 \end{aligned}$